Matched Z-transform method: Difference between revisions

Revision as of 12:23, 5 May 2014

Revision as of 17:10, 21 April 2015

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[[File:Chebyshev s plane.svg|right|thumb|The ''s''-plane poles and zeros of a 5th-order [[Chebyshev filter#Type II Chebyshev filters|Chebyshev type II lowpass filter]] to be approximated as a discrete-time filter]]

[[File:Chebyshev mapped z plane.svg|right|thumb|The ''z''-plane poles and zeros of the discrete-time Chebyshev filter, as mapped into the z-plane using the matched Z-transform method with ''T'' = 0.1/10 second. The labeled frequency points and band-edge dotted lines have also been mapped through the function exp(''sTz=e^iωT''), to show how frequencies along the ''iω'' axis in the ''s''-plane map onto the unit circle in the ''z''-plane.]]

The '''matched Z-transform method''', also called the '''pole–zero mapping'''<ref>

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}}</ref> is a technique for converting a [[continuous-time]] filter design to a [[discrete-time]] filter ([[digital filter]]) design.

The method works by mapping all poles and zeros of the [[Laplace transform|s-plane]] design to [[Z-transform|z-plane]] locations ''z'' = exp(''e^sT''), for a sample interval ''T''.<ref>

{{cite book

| title = Signal processing: principles and implementation

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Alternative methods include the [[bilinear transform]] and [[impulse invariance]] methods.

[[File:Chebyshev responses.svg|left|thumb|350px|Responses of the filter (dashed), and its discrete-time approximation (solid), for nominal cutoff frequency of 1 Hz, sample rate 1/T = 10 Hz. The discrete-time filter does not reproduce the Chebyshev equiripple property in the stopband due to the interference from cyclic copies of the response.]]

==References==